QuanTAlib/lib/trends/alma/Alma.md

ALMA: Arnaud Legoux Moving Average

"If you want to smooth data without looking like you're driving using the rear-view mirror, you use a Gaussian filter. ALMA is that filter, dressed up for Wall Street."

ALMA (Arnaud Legoux Moving Average) is a superior alternative to the standard SMA or EMA. It uses a Gaussian distribution to determine the weights of the moving average, allowing you to shift the "center of gravity" of the window. This gives you control over the trade-off between smoothness and responsiveness that other averages can only dream of.

Historical Context

Developed by Arnaud Legoux and Dimitris Kouzis-Loukas in 2009, ALMA was a response to the inherent lag in traditional moving averages. While Hull (HMA) and Jurik (JMA) tried to solve lag through complex algorithms, Legoux went back to signal processing basics: the Gaussian filter. It's elegant, mathematically sound, and doesn't rely on "magic numbers."

Architecture & Physics

ALMA is essentially a Finite Impulse Response (FIR) filter with Gaussian coefficients. Unlike an SMA (rectangular window) or WMA (triangular window), ALMA uses a bell curve.

The "physics" of ALMA are defined by three parameters:

1. Period: The window size.
2. Offset: Determines where the peak of the Gaussian curve sits. An offset of 0.85 (default) pushes the weight towards the most recent data, reducing lag significantly while maintaining smoothness.
3. Sigma: The standard deviation of the bell curve. A higher sigma (e.g., 6.0) makes the curve sharper, focusing weights tightly around the offset.

Mathematical Foundation

The weight W_i for the $i$-th element in the window is calculated as:

m = \text{offset} \times (\text{period} - 1) s = \frac{\text{period}}{\text{sigma}} W_i = \exp \left( - \frac{(i - m)^2}{2s^2} \right)

The ALMA value is the weighted sum of the prices divided by the sum of the weights:

\text{ALMA} = \frac{\sum_{i=0}^{N-1} P_{t-i} \cdot W_{N-1-i}}{\sum_{i=0}^{N-1} W_i}

Performance Profile

ALMA is computationally heavier than an SMA due to the exponential weights, but since these are precomputed, the runtime cost is strictly O(1) per update.

Metric	Score	Notes
Throughput	★★★★☆	Gaussian calculation per bar (precomputed weights).
Allocations	★★★★★	0 bytes; hot path is allocation-free.
Complexity	★★★☆☆	O(N) window iteration required.
Precision	★★★★★	double precision preserves Gaussian structure.

Zero-Allocation Design

ALMA precomputes the Gaussian weights in the constructor. The Update method performs a simple dot product of the price window and the weight vector, requiring no heap allocations.

Validation

Validation is performed against Skender and Ooples implementations.

Library	Status	Notes
QuanTAlib	✅	Validated.
Skender	✅	Matches GetAlma.
Ooples	✅	Matches CalculateArnaudLegouxMovingAverage.
TA-Lib	❌	Not implemented.
Tulip	❌	Not implemented.

Common Pitfalls

1. Offset Confusion: An offset of 1.0 makes it extremely responsive but noisy (essentially the current price). An offset of 0.5 makes it a centered moving average (great for smoothing, terrible for trading due to repainting if used as such, but ALMA doesn't repaint). The sweet spot is 0.85.
2. Sigma Sensitivity: A low sigma (e.g., 1.0) makes the filter look like a rectangular window (SMA). A high sigma makes it look like a spike. Keep it around 6.0.